aiqbench analysis
This research provides a rigorous statistical foundation for using heavy-tailed spectral distributions in weight matrices as a proxy for predicting deep neural network performance without access to training data. By deriving the marginal likelihood under the High-Temperature Marchenko-Pastur distribution, the authors offer a theoretically grounded method to detect over-fitting across large-scale convolutional networks and LLMs. This work advances the field by replacing heuristic metrics with mathematically justified tools for model quality assessment.
Why Heavy-Tailed Weight Spectra Predict Model Quality
arXiv:2610.13123v1 Announce Type: cross Abstract: A solid understanding of the predictive success of deep neural networks (DNNs) remains elusive. For example, while many data-dependent metrics exist that seek to predict model quality of DNNs, these metrics may be expensive to compute for large datasets and/or may be impossible to compute when training datasets are not released. A practical and effective predictor of model quality involves analyzing DNN weight matrices, as prior work has established that heavy-tailed spectral distributions in trained weight matrices can be strongly predictive of model quality. However, such metrics lack a rigorous statistical justification. In this work, we aim to understand why these metrics perform well, from a statistical perspective. To do so, we employ a probabilistic framework to derive the marginal likelihood for a DNN, evaluated using only the final layer weights. Across large-scale convolutional DNNs and LLMs, we find that this marginal likelihood predicts model quality. To understand the role heavy-tailed spectra play in predictive performance, we derive the limiting log-marginal likelihood for spectra that follow the (heavy-tailed) High-Temperature Marchenko-Pastur (HTMP) distribution. We show that this limiting quantity is convex in a heaviness parameter, and we derive an optimal heaviness that empirically predicts over-fitting for large-scale DNNs.
Abstract:A solid understanding of the predictive success of deep neural networks (DNNs) remains elusive. For example, while many data-dependent metrics exist that seek to predict model quality of DNNs, these metrics may be expensive to compute for large datasets and/or may be impossible to compute when training datasets are not released. A practical and effective predictor of model quality involves analyzing DNN weight matrices, as prior work has established that heavy-tailed spectral distributions in trained weight matrices can be strongly predictive of model quality. However, such metrics lack a rigorous statistical justification. In this work, we aim to understand why these metrics perform well, from a statistical perspective. To do so, we employ a probabilistic framework to derive the marginal likelihood for a DNN, evaluated using only the final layer weights. Across large-scale convolutional DNNs and LLMs, we find that this marginal likelihood predicts model quality. To understand the role heavy-tailed spectra play in predictive performance, we derive the limiting log-marginal likelihood for spectra that follow the (heavy-tailed) High-Temperature Marchenko-Pastur (HTMP) distribution. We show that this limiting quantity is convex in a heaviness parameter, and we derive an optimal heaviness that empirically predicts over-fitting for large-scale DNNs.
Accepted at NeurIPS 2026. 34 pages, 11 figures, 4 tables
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.13123 [stat.ML]
(or arXiv:2610.13123v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.13123 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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